We study the disturbance decoupling problem for linear time invariant singular systems. We give necessary and sufficient conditions for the existence of a solution to the disturbance decoupling problem with or without stability via a proportional and derivative feedback and proportional and derivative output injection that also
makes the resulting closed-loop system regular and/or of index at most one. All results are based on canonical
reduced forms that can be computed using a complete system of invariants that can be implemented in a numerically stable way.